Textbook Problem $9$

Recall the Tom's, Inc., problem $($Chapter $2,$ Problem $28).$ The firm use three types of raw materials $($whole tomatoes, tomato

sauce and tomato paste to make two salsa of products: Western Foods Salsa, and Mexico City Salsa. Per unit profit from the two

types of products are $$1$ and $$1\mathrm{.}25.$ There are availability constraints $($in pounds$)$ on each material. Letting

$W=$ jars $of$ Western Foods Salsa

$M=$ jars $of$ Mexico City Salsa

leads to the formulation:

Max $1W+1\mathrm{.}25M$ maximize total profit

$s.t.$

$5W+7M4480$ Whole tomatoes

$3W+1M2080$ Tomato sauce

$2W+2M1600$ Tomato paste

$W,M0$

The computer solution is shown in Figure $3\mathrm{.}15.$

a$.$ What is the optimal solution, and what is the optimal profit?

b$.$ Specify the objective function ranges $($range of optimality$).$

c$.$ What are the dual values for each constraint? Interpret each.

d$.$ Identify each of the right$-$hand$-$side ranges.

FIGURE $3\mathrm{.}15$ THE SOLUTION FOR THE TJ INC.$\text{'}$S PROBLEM

Additional optional textbook problems for practice $($no need to turn in$)$: $1,2,4,5,10,12,16$ and $18.$